The influence on properties of nonlinear Alfven waves produced by the introduction of a small quantity of hot anisotropic ions into the cold background plasma is studied. Nonlinear equations are obtained which describe the evolution of Alfven waves propagating along magnetic field lines. The addition of a small amount of hot anisotropic ions to the cold plasma results in a qualitative modification of the evolution equations in comparison with those obtained for a cold two-species plasma. A characteristic feature of the system is that a nonlinear stage of evolution is accompanied by the appearance of an electric field directed along the external magnetic field. Some specific solutions of these nonlinear equations are given. The stability of finite-amplitude monochromatic waves during the small-amplitude phase and in the presence of amplitude modulations is investigated.